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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
 
 
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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes [Paperback]

Daniel Solow (Author)
4.2 out of 5 stars  See all reviews (9 customer reviews)

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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes How to Read and Do Proofs: An Introduction to Mathematical Thought Processes 4.5 out of 5 stars (2)
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Book Description

0471680583 978-0471680581 October 25, 2004 4
An easy-to-use guide that shows how to read, understand, and do proofs.
  • Shows how any proof can be understood as a sequence of techniques.
  • Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction.
  • Explains how to identify which techniques are used and how they are applied in the specific problem.
  • Illustrates how to read written proofs with many step-by-step examples.
  • Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

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Editorial Reviews

Review

"I think that Solow has written an excellent text that I will highly recommend as a supplementary text for several upper division mathematics courses including abstract algebra and mathematical analysis." (Phillip Bean, Mercer University)

"His already fine book becomes more usable by having the four subject-targeted appendices." (Richard Delaware, UMKC)

"The book covers all the basic proof techniques in a very readable, concise way without overwhelming the student. The organization is great. I like the short chapters highlighting only one concept at a time." (Josephine Hamer, Western Connecticut State University)

"Very clear, rigorous, extremely thorough, almost unique in what it tries to do, reaches out to weaker students." (Michael Thaddeus, Columbia University)

From the Back Cover

Learn how to read, understand, and do proofs!

Daniel Solow’s new Fourth Edition of HOW TO READ AND DO PROOFS will help you master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once you have a firm grasp of the techniques, you’ll be better equipped to read, understand and actually do proofs. You’ll learn when each technique is likely to be successful, based on the form of the theorem.

This Fourth Edition features quick reference summaries of the proof techniques on the front and back covers, a new forward uniqueness method, a new section on counterexamples, and four new appendices in discrete mathematics, linear algebra, modern algebra, and real analysis that illustrate how the various proof techniques from the body of the text arise in doing actual mathematics.

Critical acclaim

“I think that Solow has written an excellent text that I will highly recommend as a supplementary text for several upper division mathematics courses including abstract algebra and mathematical analysis.”––Phillip Bean, Mercer University

“His already fine book becomes more usable by having the four subject-targeted appendices.”––Richard Delaware, UMKC

“The book covers all the basic proof techniques in a very readable, concise way without overwhelming the student. The organization is great. I like the short chapters highlighting only one concept at a time.”––Josephine Hamer, Western Connecticut State University

“Very clear, rigorous, extremely thorough, almost unique in what it tries to do, reaches out to weaker students.”––Michael Thaddeus, Columbia University


Product Details

  • Paperback: 288 pages
  • Publisher: Wiley; 4 edition (October 25, 2004)
  • Language: English
  • ISBN-10: 0471680583
  • ISBN-13: 978-0471680581
  • Product Dimensions: 6.2 x 0.4 x 9.4 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #345,491 in Books (See Top 100 in Books)

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Customer Reviews

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Average Customer Review
4.2 out of 5 stars (9 customer reviews)
 
 
 
 
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49 of 49 people found the following review helpful:
5.0 out of 5 stars An Excellent Rescource, September 29, 2005
This review is from: How to Read and Do Proofs: An Introduction to Mathematical Thought Processes (Paperback)
"How to Read and Do Proofs" is a magnificent introduction to mathematical thought processes. If you have always wanted to understand how to read and do your own proofs, this book will definitely provide you with the tools. This book is very thorough, and after having mastered it you will feel very comfortable about your abilities to read and construct proofs. Solow covers what he calls the "foward-backward" method first to give the reader a general understanding of how direct proof works. He then explains direct proof of existential quantifiers (there exists...), direct proof of universal quantifiers, proof by contradiction, proof by contrapositive, mathematical induction and more. He also has added 4 appendices pertaining to Modern Albebra, Analysis, Number Theory, and Linear Algebra. Many answers to exercises are provided either in the book or on-line. An excellent rescource for anyone wanting to learn the methods of mathematical proof.
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36 of 37 people found the following review helpful:
5.0 out of 5 stars Outstanding math book, and great intro to proofs, March 30, 2006
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This review is from: How to Read and Do Proofs: An Introduction to Mathematical Thought Processes (Paperback)
This is a great book, and one of my favorite math books. Like the other reviewer, I also wanted to learn how to read and write proofs. I am an engineer, (many years ago), and not a mathematician, (but really enjoy math). The author communicates clearly, and provides lots of good examples. But the heart of the book is the problem sets for each chapter. Most books on proofs spend way too much time on Logic, (or geometry), and not enough on "math" proofs. The book provides problems from a wide variety of math areas. The latest edition added a lot of new material. I struggled at times, since I went through the whole book without an instructor, and worked on all of the problems. So having most of the possible answers in the back of the book, or on the internet helped as a check on my understanding. This book would make a great gift.
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11 of 12 people found the following review helpful:
5.0 out of 5 stars A MUST HAVE!!!!!, November 7, 2006
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CNote (Phila, PA USA) - See all my reviews
This review is from: How to Read and Do Proofs: An Introduction to Mathematical Thought Processes (Paperback)
I wish this book was out when I was an undergrad! It is clear and concise. It covers many of the basic areas of math and gives a tremendous amount of insight on which style of proof fits a particular situation. Every example is presented in a very clear way, which gave me confidence in my ability to write proofs. This book should be used by ALL professors who teach an introductory analysis course.
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Inside This Book (learn more)
First Sentence:
The objective of mathematicians is to discover and to communicate certain truths. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
contrapositive method, condensed proof, recognizing the key words, overlapping notation, infimum property, backward statement, uniqueness method, contradiction method, object with the certain property, sentence challenging, backward process, nested quantifiers, first quantifier, specialization methods, one such object, initial integer, forward process, choose method, forward statement, one particular object, working forward
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Note, Least Integer Principle, World Wide Web, Examples of Proofs, Proof Reading, Real Line, Summary Creating, Use Exercise, Method Assume Conclude Forward
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